Single and Multiple Objective Optimization (Paperback)

Single and Multiple Objective Optimization covers a wide range of
techniques for optimizing functions. Single objective optimization
examines functions and identifies the function minima and maxima
over a predetermined range. Single objective optimization is often
handled using differential calculus. However, in many applications,
obtaining extrema using the methods of calculus is intractable. In
these cases alternate techniques are required. Many artificial
intelligence techniques are based on identifying a global minimum
or maximum when multiple extrema exist. Evolutionary algorithms
such as genetic algorithms, differential evolution, and particle
swarm optimization were developed as modern alternatives to the
standard optimization approaches such as differentiation and
Newton's method. These evolutionary techniques are examined and
compared against a suite of test functions to measure performance
of each technique under a variety of operating conditions.
Multiobjective optimization does not typically result in a single
optimum value. Instead, a set of incomparable points is identified
on the Pareto frontier. These points are not comparable to each
other, but are superior to other potential solutions. Although a
single operating point is not identified, the optimal value must be
among the points in the Pareto frontier. Techniques for identifying
the Pareto frontier are examined and tested using a suite of test
problems. Some of the techniques examined are the weighted sum
method, Normal-Boundary Intersection (NBI), Normal Constraint,
Strength Pareto Evolutionary Algorithm (SPEA2), Nondominated
Sorting Genetic Algorithm (NSGA2), and Directed Search Domain
(DSD). These techniques may be compared in terms of the number of
function evaluations, the distribution of points on the frontier,
the number of frontier points identified, along with many other
performance measures.